U.S. patent application number 12/083020 was filed with the patent office on 2009-05-14 for method for mechanical and capillary seal analysis of a hydrocarbon trap.
Invention is credited to Scott A. Barboza, John Steven Davis, William R. James, Xiaoli Liu, Jean Christophe Sempere.
Application Number | 20090125238 12/083020 |
Document ID | / |
Family ID | 36113813 |
Filed Date | 2009-05-14 |
United States Patent
Application |
20090125238 |
Kind Code |
A1 |
Barboza; Scott A. ; et
al. |
May 14, 2009 |
Method for Mechanical and Capillary Seal Analysis of a Hydrocarbon
Trap
Abstract
Method for making a probabilistic determination of total seal
capacity for a hydrocarbon trap, simultaneously considering both
capillary entry pressure and mechanical seal capacity, and where
capillary entry pressure is estimated by relating it directly to
the buoyancy pressure applied by the hydrocarbon column to the top
seal. The method thus considers the substantial uncertainty
associated with input parameters, which uncertainty limits the
utility of such analyses for robust hydrocarbon column height and
fluid contact predictions. The method disclosed for estimating seal
capillary entry pressure, the requisite input parameter for
capillary seal capacity analysis, by inverting trap parameters
avoids the need for direct measurement by mercury injection
capillary capacity tests on small pieces of rock, which test
results often are not available for all desired locations nor are
they necessarily representative of adjacent rocks in the seal.
Inventors: |
Barboza; Scott A.; (Houston,
TX) ; Davis; John Steven; (Kingwood, TX) ;
James; William R.; (Austin, TX) ; Sempere; Jean
Christophe; (Houston, TX) ; Liu; Xiaoli;
(State College, PA) |
Correspondence
Address: |
Matthew T. Shanley;(CORP-URC-352)
ExxonMobil Upstream Research Company, P.O. Box 2189
Houston
TX
77252-2189
US
|
Family ID: |
36113813 |
Appl. No.: |
12/083020 |
Filed: |
September 12, 2006 |
PCT Filed: |
September 12, 2006 |
PCT NO: |
PCT/US2006/035416 |
371 Date: |
August 13, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60731095 |
Oct 28, 2005 |
|
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Current U.S.
Class: |
702/11 |
Current CPC
Class: |
E21B 49/00 20130101;
E21B 47/00 20130101 |
Class at
Publication: |
702/11 |
International
Class: |
E21B 49/00 20060101
E21B049/00 |
Claims
1. A method for evaluating seal capacity in order to determine
hydrocarbon column heights (and optionally associated probable
errors) for a subject hydrocarbon trap containing oil, gas, or both
oil and gas, said method comprising: (a) estimating a
probability-weighted distribution for capillary entry pressure
values at one or more calibration locations by equating capillary
entry pressure with hydrocarbon buoyancy estimated through
inversion of pressure data and trap geometry; (b) estimating a
probability-weighted distribution for hydraulic fracture pressure
values from calculations using theoretical calculation or from
empirical data collected from one or more calibration locations;
(c) obtaining probability-weighted distributions for anticipated
fluid properties and trap geometry parameters at the subject
hydrocarbon trap, said properties and parameters including: (1)
in-situ fluid (gas, oil, and brine) density; (2) reservoir
pressure; (3) reservoir temperature; (4) trap geometry, including
crest and spill depths; (d) determining a current realization value
for each of the fluid properties and trap geometry parameters of
the subject trap by randomly selecting from their respective
probability-weighted distributions; (e) determining a current
realization value for the subject trap's capillary entry pressure
by: randomly selecting a capillary entry pressure value from the
probability-weighted distribution determined for the one or more
calibration locations; and adjusting the selected capillary entry
pressure value by calculating interfacial tensions consistent with
the subject hydrocarbon trap's pressure, temperature, and fluid
composition selected for the current realization; (f) determining a
current realization value for the subject trap's hydraulic fracture
pressure by: randomly selecting a hydraulic fracture pressure value
from the probability-weighted distribution determined by
calculation or empirical data from one or more calibration
locations; and adjusting the selected hydraulic fracture pressure
value consistent with the trap crest depth selected for the current
realization, thereby generating an adjusted fracture pressure
gradient; (g) calculating a column height for each hydrocarbon
phase (oil and gas) present in the subject trap using the randomly
selected fluid properties and trap geometry parameters of the
subject trap for the current realization, said calculation equating
hydrocarbon buoyancy with total seal capacity, said total seal
capacity being obtained by combining the adjusted hydraulic
fracture pressure gradient and capillary entry pressure values
determined for the current realization; (h) repeating steps (d)-(g)
a predetermined number of times; and (i) averaging the results and
optionally calculating an uncertainty for each column height from
spread within the results.
2. The method of claim 1, wherein estimating a probability-weighted
distribution for capillary entry pressure values at a calibration
location comprises: (a) obtaining probability-weighted
distributions for fluid properties and trap geometry parameters at
the calibration location; (b) randomly selecting a current
realization value for each said fluid property and trap geometry
parameter from their probability-weighted distributions; (c)
estimating gas entry pressure (GEP) from hydrocarbon column
buoyancy using the current realization values of the fluid
properties and trap geometry parameters; (d) optionally estimating
implied mercury injection capillary pressure (MICP) using the
current realization values of the fluid properties and trap
geometry parameters and by calculating brine-gas interfacial
tensions; (e) calculating oil entry pressure (OEP) from the gas
entry pressure; and (f) repeating steps (b)-(e) a pre-selected
number of times, averaging the results and estimating a
probability-weighted distribution for GEP, OEP and, optionally,
MICP.
3. The method of claim 1, wherein the empirical data for estimating
a probability-weighted distribution for hydraulic fracture pressure
values is leak-off test data.
4. The method of claim 1, wherein the theoretical calculation for
estimating a probability-weighted distribution for hydraulic
fracture pressure values uses critical-state soil mechanics to
solve a minimum stress equation in which hydraulic fracture
pressure is approximated by minimum horizontal stress.
5. The method of claim 4, wherein the minimum horizontal stress
.sigma..sub.h min is calculated from .sigma..sub.h
min=k.sub.o.sigma..sub.eff+P.sub.pore where k o = .sigma. 3 - P
pore .sigma. 1 - P pore ##EQU00026## and
.sigma..sub.eff=P.sub.Lith-P.sub.Pore, and P.sub.Pore is pore
pressure, P.sub.Lith is lithostatic pressure, .sigma..sub.3 is
minimum compressive stress and .sigma..sub.1 is maximum compressive
stress.
6. The method of claim 1, wherein the probability-weighted
distribution for randomly selecting a hydraulic fracture pressure
value is obtained from empirical fracture pressure data by: (a)
determining a best-fit straight line in a least-squares sense for a
plot of the empirical fracture pressure data vs. depth; (b)
determining 68.3% confidence interval curves for the said best-fit
line; and (c) using values of the best-fit line and the confidence
interval curves at the subject trap's crest depth to determine a
Gaussian probability distribution of fracture pressure values.
7. The method of claim 1, wherein the probability-weighted
distribution for randomly selecting a hydraulic fracture pressure
value is calculated by: (a) selecting a theoretical model of
fracture pressure vs. depth; (b) using said model to determine most
likely, minimum and maximum values of fracture pressure at the
crest depth of the subject trap; (c) creating a triangular
probability distribution of fracture pressure values from said most
likely, minimum and maximum fracture pressure values.
8. A method for determining capillary entry pressure for a
hydrocarbon trap from hydrocarbon contact depths and fluid
densities, said capillary entry pressure being specified by a gas
entry pressure, an oil entry pressure and, optionally, a
mercury-injection capillary pressure, said method comprising: (a)
estimating gas entry pressure from groundwater aquifer buoyancy
pressure on the hydrocarbon trap's hydrocarbon column, said
buoyancy pressure being determined from the hydrocarbon contact
depths and fluid densities; (b) calculating interfacial tension for
a gas-water interface and for an oil water interface and,
optionally, for a mercury-air interface, said interfacial tensions
being calculated for conditions representative of the trap and its
fluids; and (c) calculating oil entry pressure and, optionally,
mercury-injection capillary pressure from the gas entry pressure
and the interfacial tensions.
9. The method of claim 8, wherein determining the buoyancy of the
hydrocarbon column in the course of estimating gas entry pressure
step comprises: (a) obtaining hydrocarbon depth and fluid density
data from a measured interval (calibration location); (b)
developing a black oil empirical model of hydrocarbon fluid
properties; (c) selecting an aquifer composition model and gas
equation of state that may be used to correct aquifer and gas
densities for variations in pressure and temperature; (d) adjusting
input parameters of the black oil model and the aquifer composition
model to match measured in situ well bore fluid densities; (e)
adjusting fluid gradients as a function of pressure and temperature
within the trap using the said models to extrapolate away from the
measured interval to the trap, yielding hydrocarbon and aquifer
depth vs. pressure curves at the trap's structural crest; and (f)
deducing hydrocarbon buoyancy pressure from differences between the
aquifer depth-pressure curve and the hydrocarbon depth-pressure
curve.
10. The method of claim 8, wherein the interfacial tension
(.eta..sub.ij) at an interface between substance i and substance j
is calculated from
.eta..sub.ij=[.DELTA..rho..sub.ij(T.sub.pr).sup.-0.3125.tau.].sup.4
where
.tau.=e.sup.[0.091251n(.DELTA..rho.).sup.2.sup.-0.538331n(.DELTA..r-
ho.)+1.227328], and .DELTA..rho. is the density difference between
substance i and substance j, and where i,j refer to gas-water,
oil-water or mercury-air interfaces.
11. The method of claim 8, wherein the oil entry pressure OEP and,
optionally, the mercury injection capillary pressure MICP are
calculated from the gas entry pressure GEP and the interfacial
tensions (.eta.) using the equations M I C P .eta. Hg - air cos
.theta. Hg - air = O E P .eta. B - O cos .theta. B - O = G E P
.eta. B - G cos .theta. B - G ##EQU00027## where .theta..sub.ij is
contact angle for interfacing fluids i-j, where i and j refer to
brine or water (B), oil (O), gas (G), mercury (Hg) or air.
12. The method of claim 1, wherein hydrocarbon buoyancy is
estimated in a groundwater aquifer by: (a) obtaining hydrocarbon
depth and fluid density data from said one or more calibration
locations; (b) developing a black oil empirical model of
hydrocarbon fluid properties; (c) selecting an aquifer composition
model and gas equation of state that may be used to correct aquifer
and gas densities for variations in pressure and temperature; (d)
adjusting input parameters of the black oil model and the aquifer
composition model to match measured in situ well bore fluid
densities; (e) adjusting fluid gradients as a function of pressure
and temperature within the trap using the said models to
extrapolate away from the one or more calibration locations to the
trap, yielding hydrocarbon and aquifer depth vs. pressure curves at
the trap's structural crest; and (f) deducing hydrocarbon buoyancy
pressure from differences between the aquifer depth-pressure curve
and the hydrocarbon depth-pressure curve.
13. The method of claim 1, wherein said capillary entry pressure
consists of a gas entry pressure, an oil entry pressure (or one of
these for a single-hydrocarbon-phase trap), and, optionally, a
mercury injection capillary pressure, and gas entry pressure is
estimated from hydrocarbon column buoyancy, and oil entry pressure
and, optionally, mercury injection capillary pressure are
calculated from the gas entry pressure and interfacial tension
(.eta.) using the relationship M I C P .eta. Hg - air cos .theta.
Hg - air = O E P .eta. B - O cos .theta. B - O = G E P .eta. B - G
cos .theta. B - G ##EQU00028## where .theta..sub.ij is contact
angle for interfacing fluids i and j, and where interfacial tension
(.theta..sub.ij) at an interface between substance i and substance
j is calculated from
.eta..sub.ij=[.DELTA..rho..sub.ij(T.sub.pr).sup.-0.3125.tau.].sup.4
where
.tau.=e.sup.[0.091251n(.DELTA..rho.).sup.2.sup.-0.538331n(.DELTA..r-
ho.)+1.227328], T.sub.pr is pseudo-reduced temperature calculated
from the black-oil correlations, and .DELTA..rho. is the density
difference between substance i and substance j, and where i,j refer
to gas-water (B-G), oil-water (B-O) or mercury-air (Hg-air)
interfaces.
14. The method of claim 13, wherein gas entry pressure GEP is
estimated from hydrocarbon column buoyancy using the relationship:
GEP=.rho..sub.Bg(D.sup.OWC-D.sup.TOC)-[.rho..sub.Og(D.sup.OWC-D.sup.GOC)+-
.rho..sub.Gg(D.sup.GOC-D.sup.TOC)] where .rho. is density for
fluids brine (subscript B for brine (water)), oil (subscript O) and
gas (subscript G); g is acceleration due to gravity; and D is depth
to oil-water contact (superscript OWC), gas-oil contact
(superscript GOC) and top of the hydrocarbon column (superscript
TOC).
15. A method for producing hydrocarbons from a subterranean
formation, comprising: (a) obtaining identification of one or more
hydrocarbon traps in the formation; (b) obtaining evaluation of
seal capacity and hydrocarbon column heights for said one or more
hydrocarbon traps, said evaluation having used the method of claim
1; (c) obtaining an assessment of the hydrocarbon traps for
commercial potential based on the evaluation of the previous step;
and (d) producing hydrocarbons from a trap showing commercial
potential.
Description
[0001] This application claims the benefit of U.S. Provisional
Patent Application No. 60/731,095 filed on Oct. 28, 2005.
FIELD OF THE INVENTION
[0002] This invention relates generally to the field of hydrocarbon
exploration and production, and more particularly to hydrocarbon
system analysis. Specifically, the invention is a method for
predicting total hydrocarbon column height and contacts in a
hydrocarbon trap.
BACKGROUND OF THE INVENTION
[0003] Oil and gas deposits tend to occur in geological
configurations called traps. Buoyant forces support an oil layer on
top of the denser ground water, and similarly a gas layer floats on
top of the oil layer. A trap is a geologic configuration that
"seals" the hydrocarbon columns in place, preventing their escape.
Such escape could result either from fracture of the seal due to
hydrocarbon pressure or by capillary seepage through the seal. Such
traps often contain commercial deposits of oil or gas. In
evaluating such a trap, whether a prospect trap in the course of
exploration or a trap of interest in the course of field
development, the depths of the gas/oil contact and the oil/water
contact are key quantities of interest. These contact depths will
depend significantly on the seal capacity, i.e. the ability of the
seal to resist fracturing and capillary seepage.
[0004] Understanding and predicting total hydrocarbon column height
(difference in depth between the hydrocarbon-water contact and the
top of the hydrocarbon column) and contacts in a hydrocarbon trap
occupies the attention of every hydrocarbon exploration or
production company. Seal capacity, which is the maximum hydrocarbon
column height a seal can hold before leaking, is typically
evaluated on a deterministic basis with little consideration of the
substantial uncertainty associated with input parameters.
Furthermore, the seal is typically evaluated for either mechanical
seal capacity or capillary seal capacity without considering both
simultaneously. Also, seal capillary entry pressure, the requisite
input parameter for capillary seal capacity analysis, is usually
directly measured by mercury injection capillary capacity tests on
small pieces of rock. Results from these tests are not readily
available everywhere, nor are they necessarily representative of
adjacent rocks in the seal.
SUMMARY OF THE INVENTION
[0005] In one embodiment, the invention is a method for evaluating
seal capacity in order to determine hydrocarbon column heights (and
optionally associated probable errors) for a subject hydrocarbon
trap containing oil, gas, or both oil and gas, said method
comprising: (a) estimating a probability-weighted distribution for
capillary entry pressure values at one or more calibration
locations by equating capillary entry pressure with hydrocarbon
buoyancy estimated through inversion of pressure data and trap
geometry; (b) estimating a probability-weighted distribution for
hydraulic fracture pressure values from calculations using
theoretical calculation or from empirical data collected from one
or more calibration locations; (c) obtaining probability-weighted
distributions for anticipated fluid properties and trap geometry
parameters at the subject hydrocarbon trap, said properties and
parameters including:
[0006] (1) in-situ fluid (gas, oil, and brine) density;
[0007] (2) reservoir pressure;
[0008] (3) reservoir temperature;
[0009] (4) trap geometry, including crest and spill depths;
(d) determining a current realization value for each of the fluid
properties and trap geometry parameters of the subject trap by
randomly selecting from their respective probability-weighted
distributions; (e) determining a current realization value for the
subject trap's capillary entry pressure by: randomly selecting a
capillary entry pressure value from the probability-weighted
distribution determined for the one or more calibration locations;
and adjusting the selected capillary entry pressure value by
calculating interfacial tensions consistent with the subject
hydrocarbon trap's pressure, temperature, and fluid composition
selected for the current realization; (f) determining a current
realization value for the subject trap's hydraulic fracture
pressure by: randomly selecting a hydraulic fracture pressure value
from the probability-weighted distribution determined by
calculation or empirical data from one or more calibration
locations; and adjusting the selected hydraulic fracture pressure
value consistent with the trap crest depth selected for the current
realization, thereby generating an adjusted fracture pressure
gradient; (g) calculating a column height for each hydrocarbon
phase (oil and gas) present in the subject trap using the randomly
selected fluid properties and trap geometry parameters of the
subject trap for the current realization, said calculation equating
hydrocarbon buoyancy with total seal capacity, said total seal
capacity being obtained by combining the adjusted hydraulic
fracture pressure gradient and capillary entry pressure values
determined for the current realization; (h) repeating steps (d)-(g)
a predetermined number of times; and (i) averaging the results and
optionally calculating an uncertainty for each column height from
spread within the results.
[0010] In one embodiment of the invention, the step above of
estimating a probability-weighted distribution for capillary entry
pressure values at a calibration location comprises: (a) obtaining
probability-weighted distributions for fluid properties and trap
geometry parameters at the calibration location; (b) randomly
selecting a current realization value for each said fluid property
and trap geometry parameter from their probability-weighted
distributions; (c) estimating gas entry pressure (GEP) from
hydrocarbon column buoyancy using the current realization values of
the fluid properties and trap geometry parameters; (d) optionally
estimating implied mercury injection capillary pressure (MICP)
using the current realization values of the fluid properties and
trap geometry parameters and by calculating brine-gas interfacial
tensions; (e) calculating oil entry pressure (OEP) from the gas
entry pressure; and (f) repeating steps (b)-(e) a pre-selected
number of times, averaging the results and estimating a
probability-weighted distribution for GEP, OEP and, optionally,
MICP.
[0011] In some embodiments of the invention, the theoretical
calculation for estimating a probability-weighted distribution for
hydraulic fracture pressure values uses critical-state soil
mechanics to solve a minimum stress equation in which hydraulic
fracture pressure is approximated by minimum horizontal stress.
[0012] The invention's method for determining capillary entry
pressure may be used by itself in a deterministic calculation of
capillary entry pressure for a hydrocarbon trap from hydrocarbon
contact depths and fluid densities, the capillary entry pressure
being specified by a gas entry pressure, an oil entry pressure and,
optionally, a mercury-injection capillary pressure, the method
comprising: (a) estimating gas entry pressure from groundwater
aquifer buoyancy pressure on the hydrocarbon trap's hydrocarbon
column, said buoyancy pressure being determined from the
hydrocarbon contact depths and fluid densities; (b) calculating
interfacial tension for a gas-water interface and for an oil water
interface and, optionally, for a mercury-air interface, said
interfacial tensions being calculated for conditions representative
of the trap and its fluids; and (c) calculating oil entry pressure
and, optionally, mercury-injection capillary pressure from the gas
entry pressure and the interfacial tensions. In some embodiments,
the buoyancy of the hydrocarbon column which is needed in the
course of estimating gas entry pressure step is determined by steps
comprising: (a) obtaining hydrocarbon depth and fluid density data
from a measured interval (calibration location); (b) developing a
black oil empirical model of hydrocarbon fluid properties; (c)
selecting an aquifer composition model and gas equation of state
that may be used to correct aquifer and gas densities for
variations in pressure and temperature; (d) adjusting input
parameters of the black oil model and the aquifer composition model
to match measured in situ well bore fluid densities; (e) adjusting
fluid gradients as a function of pressure and temperature within
the trap using the said models to extrapolate away from the
measured interval to the trap, yielding hydrocarbon and aquifer
depth vs. pressure curves at the trap's structural crest; and (f)
deducing hydrocarbon buoyancy pressure from differences between the
aquifer depth-pressure curve and the hydrocarbon depth-pressure
curve.
BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The present invention and its advantages will be better
understood by referring to the following detailed description and
the attached drawings in which:
[0014] FIG. 1 illustrates that hydrostatic pressure depends only on
depth and fluid density and is independent of container shape;
[0015] FIG. 2 illustrates the meaning of typical terms used to
describe subsurface pressures;
[0016] FIG. 3 illustrates that low hydrocarbon density relative to
water creates a slower decrease in pressure with shallowing depth
within hydrocarbon columns;
[0017] FIG. 4 illustrates capillary wetting angle in a pore
throat;
[0018] FIGS. 5A-F depict various possible cases of contact and
capillary/mechanical leakage relationships;
[0019] FIG. 6 is a flowchart showing basic steps of one embodiment
of the present inventive method;
[0020] FIG. 7 is a flowchart of basic steps in one embodiment of
the present invention's method for estimating a
probability-weighted distribution for capillary entry pressure;
[0021] FIG. 8 illustrates developing a probability-weighted
distribution for a parameter (fracture pressure) from empirical
data; and
[0022] FIG. 9 illustrates developing a probability-weighted
distribution for the parameter fracture pressure from a theoretical
fracture pressure model.
[0023] The invention will be described in connection with its
preferred embodiments. However, to the extent that the following
detailed description is specific to a particular embodiment or a
particular use of the invention, this is intended to be
illustrative only, and is not to be construed as limiting the scope
of the invention. On the contrary, it is intended to cover all
alternatives, modifications and equivalents that may be included
within the spirit and scope of the invention, as defined by the
appended claims.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS
[0024] The present invention is a method for predicting mechanical
and capillary seal capacity in tandem, and propagating input
parameter uncertainties to predict the probable error of the
result. The present invention also discloses a method for
predicting top-seal capillary entry pressure based on inversion of
readily observed trap and hydrocarbon column-height parameters
combined with fluid gradients estimated from commonly available
fluid and physical properties data.
[0025] The present invention recognizes that predictions of total
hydrocarbon column height and contacts in a hydrocarbon trap
require combined evaluation of capillary and mechanical seal
properties, careful evaluation and quantification of uncertainties,
and the propagation of these uncertainties through the analysis. It
is a premise of the present invention that a seal should be
evaluated for mechanical seal capacity and capillary seal capacity
simultaneously, and that this is a requirement for robust
hydrocarbon column height and fluid contact predictions.
[0026] In the present inventive method, attention is focused on
trap-scale controls on hydrocarbon contacts. Accordingly,
hydrocarbon contact predictions are sensitive to trap geometry
(including sand connectivity resulting from structural and
stratigraphic controls) and hydrocarbon-leak potential. The present
inventive method is concerned with the evaluation of hydrocarbon
leakage from a trap with a known geometry. It may be effectively
used as a tool to help quickly evaluate trap geometry and
connectivity scenarios, propagating uncertainty through statistical
calculations. It is thus appropriate to use the present inventive
method to, among other applications, evaluate the validity of
hydrocarbon contacts for trap geometry scenarios, explore the
consequences of direct hydrocarbon indicators or proposed pre-drill
fluid contacts, or to calculate implied seal capacities in
reservoirs in which the contacts and trap geometry are fairly well
constrained. Following is a brief review of the theoretical basis
of the present inventive method.
Fluid Pressure
[0027] A complete description of subsurface hydrodynamics is not
presented because this depth of detail will be known or readily
available to persons skilled in the art from familiarity with
references such as two articles by Chapman in Studies in Abnormal
Pressure, Fertl, W. H., Chapman, R. E. and Holz, R. F., Eds.,
Elsevier, Amsterdam, Developments in Petroleum Science 38 (1994):
"The Geology of Abnormal Pore Pressures," 19-49; and "Abnormal pore
pressures: Essential theory, possible causes, and sliding,"
187-240. A few key fundamental concepts and definitions are helpful
for the discussion that follows. Normal or hydrostatic pressure is
defined as the pressure exerted by a static column of water from
the surface to the depth of interest. FIG. 1 illustrates that such
pressure depends only on vertical depth (and fluid density)
regardless of the shape of the container. The rate of change of
pressure with depth, or pressure gradient, is a function of the
fluid density. In the case of subsurface brines, hydrostatic
pressure gradients range between 0.42 and 0.47 psi/ft depending on
brine salinity and pressure (as brine is slightly
compressible).
[0028] The pressure at any depth resulting from the weight of the
overlying sediments is termed the lithostatic or overburden
pressure or stress. Typical lithostatic pressure gradients range
between 0.7-1.2 psi/ft. In a hydrostatic system, the overburden
stress is transmitted by the grain-grain contacts in the sediments
and the hydrostatic stress is transmitted by the brine within the
interconnected pore network. The overburden stress causes the
sediment to compact, collapsing the pore network and expelling
brine from the pore space. In low permeability sediments, brine
expulsion is impeded, so the pore fluid may begin to support some
of the overburden stress causing the pore pressure to be elevated
above hydrostatic. The portion of the overburden stress supported
by the grain-grain contacts in the rock is termed the effective
stress and the portion supported by the pore fluid is termed the
overpressure (or excess pressure). FIG. 2 is a graph of overburden
stress 21 relative to hydrostatic (normal) pressure 22. Pore
pressure is indicated by 23. Thus, effective stress 24 and
overpressure (excess pressure) 25 may be read from the graph.
[0029] Practically, pore pressures approach a mechanical limit
somewhat less than the lithostatic pressure or stress
(.sigma..sub.L) called the fracture pressure (P.sub.f), or the
fluid pressure at which hydrofractures begin to form in a rock.
This can be seen in FIG. 2. The magnitude by which .sigma..sub.L
exceeds P.sub.f depends on the orientation of maximum compressive
stress (.sigma..sub.1). In extensional or quiescent environments,
.sigma..sub.L=.sigma..sub.1 and P.sub.f=.sigma..sub.L, whereas in
contractional settings, .sigma..sub.L.noteq..sigma..sub.1 and
P.sub.f.apprxeq..sigma..sub.L.
[0030] It is important to recognize that over-pressured systems are
dynamic and high overpressure means a high potential for brine
flow. The magnitude of the pore pressure will depend on the burial
rate (increasing the overburden stress), the stratigraphy, and the
rate of brine expulsion. So systems with a high burial rate and/or
a low permeability will tend to generate higher excess pressures
and lower effective stresses.
[0031] In multiphase fluid systems, density differences between
phases lead to buoyant segregation of fluid phases (FIG. 3). In
hydrocarbon systems, hydrocarbon liquids and gases, being less
dense than formation brines, will have a lower pressure gradient
and higher absolute pressures than the aquifer. This pressure
difference is a function of the hydrocarbon density and column
height (the vertical height of the different hydrocarbon fluid
phases in the trap) and is the measure of the fluid potential for
secondary hydrocarbon migration. Typical hydrocarbon pressure
gradients are .about.0.3 psi/ft for oil and .about.0.1 psi/ft for
gas. In FIG. 3, the oil-water cutoff (interface) is 31 and the
gas-oil cutoff is 32. Line 33 shows the more gradual decline in
pressure with decreasing depth within the hydrocarbon column 36 as
compared to a hypothetical water column represented by line 35
which represents hydrostatic pressure alone, and line 34 which
shows the increased pressure, called overpressure 37, due to the
weight of the overburden. Line 38 denotes the buoyant pressure. The
pressure gradient in each medium is the slope of the respective
pressure vs. depth line.
Mechanical Seal Capacity
[0032] Mechanical seal capacity refers to the size of the
hydrocarbon column that achieves a hydraulic pressure at the top of
column equaling or exceeding the hydraulic fracture pressure of the
overlying seal. At mechanical seal capacity hydrocarbons migrate
through the seal at the top of column. A complete description of
subsurface mechanical seal capacity is not presented because this
depth of detail will be known or readily available to persons
skilled in the art. For a description of rock fracture mechanics
models, see, for example, Simmons and Rau, "Predicting Deepwater
Fracture Pressures: A Proposal," paper SPE 18025, 1988 SPE Annual
Technical Conference and Exhibition, Houston, Oct. 2-5; or Rocha
and Bourgoyne, "A new simple method to estimate fracture pressure
gradient," Pore pressure and fracture gradients [Serial] SPE
Reprint Series, 101-107 (1999). Following are a few key fundamental
concepts and definitions.
[0033] Hydraulic seal failure is typically associated with three
geologic environments: [0034] Shallow reservoirs [0035] Highly over
pressured reservoirs [0036] Very large hydrocarbon columns
[0037] The key parameter controlling hydraulic seal failure is the
minimum effective stress. The effective stress is defined as the
difference between the minimum principal compressive stress and the
pore fluid pressure. The minimum compressive stress is commonly
horizontal, but can be oriented in different directions depending
on the geologic environment. Hydraulic seal failure occurs when the
effective stress in a particular portion of the stratigraphic
section approaches zero (approaches a tensile regime). The vertical
compressive stress (due to overburden) always increases with depth
in sedimentary basins, but the effective stress may increase or
decrease with depth due to other factors.
[0038] At low effective stress, small disturbances in the stress
field can hydraulically fracture or re-open fractures in the top
seal and result in hydrocarbon leakage. The increase in fluid
pressure caused by hydrocarbon migration into a trap can be enough
to fracture the top or fault seal. When fracturing occurs,
hydrocarbons will leak from the trap until the fluid pressure drops
below the minimum principal compressive stress, which then allows
the fractures to close and the leakage to cease. In general,
hydraulic top or fault seal failure is not catastrophic, and the
traps do not lose all hydrocarbons.
[0039] To evaluate hydraulic leakage risks, some measure of
hydrocarbon column height, hydrocarbon density, aquifer pressure,
and fracture pressure is required. There are several methods for
estimating fracture pressure, or fracture gradient, including:
[0040] Minimum Stress Methods: these are commonly used methods in
which the fracture pressure is approximated by the minimum
horizontal stress (.sigma..sub.h min). [0041] Minimum stress
methods assume stable relationships between horizontal and vertical
stresses that depend on rock properties; [0042] During burial and
compaction of sediments (during which vertical effective stress at
maximum value):
[0042] .sigma..sub.h
min=k.sub.o(.sigma..sub.1-P.sub.pore)+P.sub.pore=k.sub.o.sigma..sub.eff+P-
.sub.pore
where .sigma..sub.h min=the minimum horizontal stress,
k o = .sigma. 3 - P pore .sigma. 1 - P pore ##EQU00001##
(for a uniaxial compressive state where compaction is in one
direction with no lateral strains)=ratio of minimum and maximum
effective stress, 0.4 for strong materials to >0.8 for
shale/clay, .sigma..sub.1=the vertical stress, taken as the
sediment overburden pressure at the depth of interest, and
P.sub.pore=pore pressure. [0043] Hoop Stress Methods: these methods
are based on analytical solutions for stresses in a plate with a
circular hole (e.g., a wellbore). They predict lost returns when
the wellbore pressure causes the hoop stress along the wellbore
wall (or the stress tangential to the wellbore) to equal the rock's
tensile strength. [0044] Fracture Mechanics Methods: these methods
take detailed information about fracture toughness, initial crack
length, and fluid pressure distribution along a crack, and use that
information to determine the conditions under which fracture
propagation will begin and end. They are used to design hydraulic
fracturing treatments. [0045] Empirical methods: Minimum horizontal
stress is sometimes approximated by a best-fit to empirical
measures of the compressive stress (formation integrity test, FIT;
leak-off test, LOT; pressure integrity test, PIT; or production
data).
[0046] In complex tectonic environments, detailed estimation of
fracture gradient may require application of multiple approaches.
In many settings, however, a minimum horizontal stress method
provides adequate estimates, and its required input parameters are
commonly available. Therefore, it is one of the two fracture
gradient estimation methods, along with empirical approaches, that
are used in preferred embodiments of this invention, as described
in detail below.
Capillary Seal Capacity
[0047] A complete description of subsurface capillary seal capacity
is not presented (except for innovations of the present invention)
because this depth of detail will be known or readily available to
persons skilled in the art. Following are a few key fundamental
concepts and definitions.
[0048] Hydrocarbons move through water-saturated porous rocks due
to buoyancy. Work is required to increase the surface area of a
hydrocarbon filament so it can displace water in the pore space of
finer-grained rocks. This results in a resistance to hydrocarbon
movement. The magnitude of this resistance is a function of the
size of the smallest pore throat in the connected pathway,
wettability, and the interfacial tension between hydrocarbon and
brine. See, for example, Berg, R. R., "Capillary pressure in
stratigraphic traps," AAPG Bulletin 59, 939-956 (1975); and
Schowalter, T. T., "Mechanics of secondary hydrocarbon migration
and entrapment," AAPG Bulletin 63, 723-760 (1979). The "capillary
entry pressure" (Pc), also called the "displacement" or "threshold"
pressure, quantifies the magnitude of the resistant force for low
flow rates. See, for example, Smith, D. A., "Theoretical
considerations of sealing and non-sealing faults," AAPG Bulletin
50, 363-374 (1966).
[0049] The relevant physics is depicted in FIG. 4. Small pore
throats 41 within the finer-grained sealing unit 42 impede
hydrocarbon flow so that the underlying hydrocarbon column 43
increases. As the hydrocarbon column increases, the buoyancy of the
hydrocarbon column increases the pressure difference between the
wetting and non-wetting phase, forcing the hydrocarbons into the
water-saturated pore throat. The equilibrium
hydrocarbon-brine-solid contact is at the wetting angle. When the
hydrocarbon column height is sufficient for the buoyancy force to
equal the capillary entry pressure of the seal, hydrocarbons may
enter the pore throat 41, deforming the immiscible boundary between
the phases into a shape that fits between the pore throats of the
sealing unit.
[0050] When two immiscible fluids contact a solid surface, one
phase is preferentially attracted to the sold. Wettability is
expressed mathematically by the contact angle (wetting angle) of
the oil-water interface against the rock. This angle depends on the
degree of preferential attraction or, put another way, the work
needed to separate a wetting fluid from a solid. In some
embodiments of the present invention, it is assumed that rock
grains in natural systems are water wet, meaning that grains are
coated by a thin water film.
[0051] Interfacial tension is an expression of the work required to
enlarge by unit area the interface between two immiscible fluids.
This tension results from the difference between the mutual
attraction of like molecules within each fluid and the attraction
of dissimilar molecules across the fluid interface.
[0052] The upward pressure P.sub.c resulting from the buoyancy
force on the hydrocarbons is given by
P c . = 2 .eta. cos .theta. R ##EQU00002##
where .eta. is the hydrocarbon-water interfacial tension, .theta.
is the wetting angle at breakthrough, and R is the pore throat
radius.
Model for Prediction of Contact Elevations
[0053] Trap configuration combined with capillary entry pressure
and hydraulic fracture gradient is sufficient to determine the
location of present-day hydrocarbon contacts if various assumptions
including the following are satisfied: [0054] (a) The present-day
"geology" (geometry, rock properties, etc) is sufficient to solve
the problem. This implies that the charge rates are generally high
compared to deposition rates. This assumption is not always valid,
but experience indicates that this assumption usually does not lead
to significant errors. This assumption is most likely to be valid
for old traps and/or systems with recent hydrocarbon charge. [0055]
(b) Volumes of oil and gas sufficient to fill the accumulation have
been generated from the source and migrated to the trap (i.e., the
trap is not charge-limited for oil or gas). [0056] (c) The
hydrocarbon distribution is at a quasi steady-state equilibrium
condition. According to this assumption, migration is fast on a
geological time scale and the final hydrocarbon distribution is not
a function of the total charge volume (except that the trap is not
charge limited as stated above). The distribution of fluids is
controlled by capillary forces and is independent of the
permeability. (Capillary forces and permeability are not totally
independent, but in this model only the capillary forces are
needed.) This assumption means that at present day, the charge rate
of fluids into the trap is equal to the sum of the leakage and
spillage rates from the trap. [0057] (d) Capillary leakage occurs
at the point of highest buoyancy force for the leaking phase. (If a
trap leaks gas, it leaks at the crest; if a trap leaks oil, it
leaks at the gas-oil contact.) This has the same effect as the
slightly more restrictive assumption that the seal has uniform
capillary properties. [0058] (e) Hydraulic fracture leakage occurs
at the top of the hydrocarbon column (trap crest). [0059] (f) The
capillary (entry) pressure of the seal is not a function of fluid
saturations in the seal or the flux rate of fluids through the
seal. The seal capillary capacity changes only due to changes in
brine-hydrocarbon interfacial tension. This assumption means the
hydrocarbon distribution is not a function of the system charge
rate. [0060] (g) The contact angle is zero for oil-water and
gas-water systems (i.e., seals are completely water wet). [0061]
(h) The water phases in the seal and the trap have similar excess
pressures. Higher excess pressures in the seal increase the
effective seal capacity because the buoyancy force of the
hydrocarbon column must exceed the excess pressure as well as the
capillary entry pressure. Lower excess pressures in the seal
decrease effective seal properties by providing an additional
driving force for hydrocarbon movement. See, for example, Heum, O.
R., "A fluid dynamic classification of hydrocarbon entrapment,"
Petroleum Geoscience 2, 145-158 (1996).
[0062] If the hydrocarbons are in the two-phase region (in P-T
space) and given the above assumptions, there are six possible
leakage scenarios. These six cases are illustrated in FIGS. 5A-F.
In the vernacular of the Sales classification system, Case 6 (FIG.
5F) is equivalent to a Sales Class 1 trap, Case 4 (FIG. 5D) is
equivalent to a Sales Class 2 trap, and Case 2 (FIG. 5B) is
equivalent to a Sales Class 3 trap. Case 1 (FIG. 5A) is not
possible to realize with capillary leakage alone, so there is no
equivalent in the Sales classification system. See Sales, J. K.,
"Seal strength vs. trap closure--A fundamental control on the
distribution of oil and gas," in, Seals, Traps, and the Petroleum
System, R. C. Surdam, ed., AAPG Memoir 67, 57-83 (1997). Cases 2
and 3 (FIG. 5C) and Cases 4 and 5 (FIG. 5E) are not possible to
distinguish with hydrocarbon column heights alone.
[0063] FIGS. 5 A-F are similar in what they show to FIG. 3. Each
drawing has one line showing water pressure vs. depth and a second
line showing the more gradual increase of pressure with depth in
the hydrocarbon column. Where the hydrocarbon column includes both
gas and oil phases, the second line consists of two line segments
with different slopes. (FIGS. 5 B, C, D and E) In FIG. 5A, the
hydrocarbon column is all oil (narrow stripes) and in FIG. 5F it is
all gas (wide stripes).
[0064] In case 1 (FIG. 5A), the buoyancy pressure of the
hydrocarbon column exceeds the seal fracture pressure. Both oil and
gas leak at the crest by hydraulic fracturing and trap completely
filled with oil. In the limit where the aquifer pressure at the
crest approaches the fracture pressure (P.sub.f), the oil column
height approaches zero.
[0065] In case 2 (FIG. 5B), the buoyancy pressure of hydrocarbon
column exceeds the gas entry pressure ("GEP") at the crest and the
buoyancy of the oil leg exceeds the oil entry pressure ("OEP") at
the gas-oil contact ("GOC"). Gas and oil leak by capillary
breakthrough separately at the crest and at the elevation of the
GOC.
[0066] In case 3 (FIG. 5C), the buoyancy pressure of the
hydrocarbon column exceeds the P.sub.f at the crest and the
buoyancy of the oil leg exceeds the OEP at the GOC. Gas hydraulic
leakage occurs at the crest and oil capillary leakage occurs
through the topseal at the elevation of the GOC. Leakoff and the
OEP pressure control the GOC and the oil-water contact ("OWC"). The
small gas column at the top of the hydrocarbon column in FIGS. 5B
and 5C is indicated by 51.
[0067] In case 4 (FIG. 5D), the buoyancy pressure of the
hydrocarbon column exceeds the GEP at the crest, but the buoyancy
of the oil leg does not exceed the OEP at the GOC. Gas capillary
leakage occurs at the crest and oil spills from the trap. GEP and
closure height control GOC and OWC.
[0068] In case 5 (FIG. 5E), the buoyancy pressure of the
hydrocarbon column exceeds the P.sub.f at the crest, but the
buoyancy of the oil leg does not exceed the OEP at the GOC. Gas
hydraulic leakage occurs at the crest and oil spills from the trap.
P.sub.f and closure height control the GOC and OWC.
[0069] In case 6 (FIG. 5F), the buoyancy pressure of an all gas
column is less than the P.sub.f or the GEP. There is no leakage,
both gas and oil spill from the trap, and the only fluid phase
within the trap is gas.
Basic Method
[0070] FIG. 6 is a flowchart showing basic steps for one embodiment
of the present inventive method. First, a brief description of the
steps of the method is given, followed by treatments of some steps
in more detail.
[0071] At step 61, a probability-weighted distribution is estimated
for capillary entry pressure values at a calibration location (as
contrasted with the location of the prospect trap that is the
subject of the evaluation). Possible alternatives for performing
this step include: a) performing standard laboratory Mercury
Injection Capillary Entry Pressure (MICP) experiments on a
representative sampling of seal rocks from a calibration location,
or b) calculating a value for MICP implied by hydrocarbon column
heights at a calibration location (this preferred method is
described in more detail below).
[0072] Step 62 is estimating a probability-weighted distribution of
hydraulic fracture pressure values (i.e., a fracture gradient) at a
calibration location. Possible alternatives for performing this
step include: [0073] (a) Best Fit to Leak-off Test Data. Estimate
hydraulic fracture gradient by deriving a best fit to leak-off
pressure test data using a linear regression algorithm (described
further below). [0074] (b) Geomechanical Theory. Estimate the
hydraulic fracture gradient using critical-state soil mechanics
method incorporating externally derived overburden and pore
pressure estimates, and a k.sub.o value (lithology dependent
horizontal to vertical stress ratio) estimated from regional
experience, and/or rock type, and/or burial history (described
further below).
[0075] Step 63 is estimating a probability-weighted distribution
for trap and fluid parameters at a prospect location, most likely
based on expert opinion. [0076] (a) Trap parameters (best estimate
plus associated uncertainty ranges) [0077] i) Depth of the trap
crest [0078] ii) Depth of the trap spill and/or controlling fault
juxtaposition leaks. [0079] iii) Trap temperature [0080] (b) Fluid
parameters [0081] i) In-situ fluid (hydrocarbon, brine) density.
[0082] ii) Formation aquifer pressure
[0083] The remaining steps concern the probabilistic analysis, for
which the preceding steps provide input. The probabilistic analysis
is also discussed in more detail below. Step 64 is randomly
selecting from the three probability-weighted distributions from
steps 61-63 a capillary entry pressure value, a hydraulic fracture
pressure value, and a value for each of the trap and fluid
properties. The capillary entry pressure is derived from a
calibration location where the hydrocarbon contacts are known. In
step 65, the selected capillary entry pressure value is adjusted
for interfacial tensions consistent with pressure, temperature, and
fluid properties selected to be representative of the subject
(prospect or development) trap. In step 66, the selected hydraulic
fracture pressure is adjusted for a selected crest depth believed
to be representative of the subject trap. At step 67, hydrocarbon
column heights are calculated consistent with the selected trap
parameters, fluid parameters, and mechanical seal capacity
parameters. One random realization is now complete. At step 68,
steps 64-67 are repeated a predetermined number of times, thus
generating the desired number of random realizations. At step 69,
the stochastic results are ready for analysis by the data
interpreter.
Estimating Capillary Entry Pressure (Step 61)
[0084] Steps 61 and 62 in the FIG. 6 flowchart call for calculating
a probability-weighted distribution of capillary and mechanical
seal capacities based upon observations obtained at one or more
calibration locations. These distributions are adjusted to conform
to expected conditions at a subject location. The following
discussion discloses a preferred method for determining the
probability-weighted distribution of capillary seal capacity from a
calibration location. The method may be repeated several times if
multiple calibration locations are available. Favorable calibration
locations for capillary seal capacity analysis are preferably
selected based upon the following criteria: [0085] (a) The
calibration location and the subject location should be in the same
geographic area. [0086] (b) The components of the trap
configuration of the calibration location listed below as required
input quantities should be well constrained. [0087] (c) The top
seal (the rock type through which hydrocarbons leak) of the
calibration location should be similar to the subject top seal in
terms of lithology, texture, and effective stress.
[0088] In the afore-mentioned preferred embodiment of the present
inventive method, the seal capillary entry pressure is estimated by
inversion of commonly available hydrocarbon trap and fluid property
data. This technique is a significant departure from the existing
petroleum industry practice of directly measuring capillary-entry
pressure by mercury injection (MICP) or other techniques. These
existing techniques depend on availability of rock samples that are
representative of the weakest element of the seal or comparisons to
global databases. The method disclosed herein results in an
estimate of seal capillary-entry pressure for the weakest element
of the seal without specific identification of that element.
[0089] This method extends a model disclosed by Sales for
hydrocarbon leakage based on known subsurface fluid contacts, trap
parameters, and fluid compositions for application to the
exploration scale. See Sales, J. K., "Seal strength vs. trap
closure--A fundamental control on the distribution of oil and gas,"
in Seals, Traps, and the Petroleum System, R. C. Surdam, ed., AAPG
Memoir 67, 57-83 (1997). This empirical model may be used to
estimate the capillary seal capacity necessary for hydrocarbon
leakage to occur out of a trap with a given closure height
(so-called "implied" MICP).
[0090] A premise of the present invention's method for estimating
capillary seal capacity is that the most reliable estimates of seal
capacity are implied values from pressure data. An implied gas
entry pressure (GEP) assumes that the GEP is equal to the buoyancy
forces of the hydrocarbons in a trap that is leaking gas or gas and
oil. If the trap is not leaking, then the calculated value will be
a minimum implied GEP instead of a most likely implied GEP.
[0091] According to a quasi-steady-state equilibrium model,
capillary seal strength is related directly to the buoyancy
pressure applied by the hydrocarbon column to the top seal. The
buoyancy pressure at the crest is less than the seal capacity for
Case 6 traps and equal to the gas entry or threshold pressure for
Case 2 or 4 traps (See FIGS. 5A-F). The buoyancy pressure exerted
by the oil column at the gas-oil contact is equal to the oil entry
or threshold pressure for Case 2 or 3 traps. The gas or oil entry
pressure may be related to the seal capacity if oil-brine and
gas-brine interfacial tensions are known.
[0092] For gas entry pressure (GEP) estimation in this embodiment
of the present inventive method, the following probability-weighted
distributions are obtained and used: [0093] depth to the top of the
hydrocarbon column (D.sup.CTOC). [0094] depth to the gas-oil
contact (D.sup.CGOC). [0095] depth to the oil-water contact
(D.sup.COWC). [0096] in-situ gas density (.rho..sub.G). [0097]
in-situ oil density (.rho..sub.O). [0098] in-situ brine density
(.rho..sub.B).
[0099] For oil entry pressure (OEP) estimation in this embodiment
of the present inventive method, the following probability weighted
distributions are obtained and used: [0100] reservoir temperature
(T.sup.CGOC) at D.sup.CGOC. [0101] gas pressure (P.sub.G.sup.CGOC)
at D.sup.CGOC. [0102] probability-weighted distribution of the Z
factor (Z) (See, for example, Standing, M. B. and Katz, D. L.,
"Density of natural gases," Trans. AIME 146, 140-149 (1942)).
[0103] The flowchart of FIG. 7 shows basic steps for performing
step 61 of FIG. 6 for this embodiment of the present inventive
method:
Step 71: Random Selection of Input Parameters
[0104] A single value of each required input quantity is randomly
selected from the probability-weighted distribution for such
parameter to generate the input values for the current
realization.
Step 72: Estimate Gas Entry Pressure (GEP) for Current
Realization
[0105] The GEP (gas entry pressure) is determined from contact
elevations, trap geometry, and pressure gradients alone, and may be
used for predictions at sites with similar pressure and temperature
(P-T) conditions.
[0106] To estimate the buoyancy pressure exerted by trapped
hydrocarbons within the structure, a black-oil model (a well known
empirical model of hydrocarbon fluid properties) may be used to (1)
correct fluid gradients for changes in pressure and temperature
away from the measured interval (an untypical application of the
black-oil model) and (2) correct measured fluid gradients measured
in offset drilling to compensate for changes in temperature and
pressure at the prospect of interest (a standard application). An
aquifer composition model (salinity) and gas equation of state may
be used to correct aquifer and gas densities for variations in
pressure and temperature. Non-ideality (in the gas equation of
state) is specified by the Z factor, which may be determined
iteratively. An alternative method for correcting fluid properties
for pressure, temperature, and fluid composition is that of an EOS
(Equation of State) model. Such models are readily available to
practitioners in the field and they provide one example of an
approach that could be used as an alternative to the black oil
model methodology developed below or another empirical approach or
other method for performing this step.
[0107] This preferred embodiment of the invention operates by first
manually adjusting input parameters of the black-oil model and
aquifer composition model to match measured in-situ fluid densities
from the wellbore. Next, the fluid gradients are adjusted as a
function of absolute pressure and temperature within the trap using
the calibrated models to extrapolate away from the measured
interval, i.e. the depth range over which pressure data was
collected. The results are curves that may be used to estimate
hydrocarbon and aquifer pressure at the structural crest. The
difference between the extrapolated aquifer depth-pressure curve
and the extrapolated hydrocarbon depth-pressure curve at the crest
of the trap is a measure of the buoyancy pressure exerted by the
hydrocarbons at the structural crest.
[0108] The gas entry pressure at the depth of the top of the
hydrocarbon column at the calibration location (D.sup.CTOC) may
thus be estimated from the buoyancy of the hydrocarbon column
by:
GEP.sup.CTOC=.rho..sub.Bg(D.sup.COWC-D.sup.CTOC)-[.rho..sub.Og(D.sup.COW-
C-D.sup.CGOC)+.rho..sub.Gg(D.sup.CGOC-D.sup.CTOC)]
[0109] The oil entry pressure ("OEP") may then be calculated from
the GEP and hydrocarbon-brine interfacial tension. The MICP may be
calculated in a similar way. This calculation requires an estimate
of the gas-brine interfacial tension. Interfacial tension is
calculated from the Firoozabadi Tau, an empirical relationship
between hydrocarbon-brine density difference and interfacial
tension:
.tau.=e.sup.(0.091251n(.DELTA..rho.).sup.2.sup.-0.538331n(.DELTA..rho.)+-
1.227328),
where .DELTA..rho. is the hydrocarbon-brine density difference. The
Firoozabadi Tau may be used to estimate hydrocarbon-brine
interfacial tension through the relationship:
.eta..sub.B-HC=[.DELTA..rho..sub.B-HC(T.sub.pr.sup.HC).sup.-0.3125.tau.]-
.sup.4,
where T.sub.pr.sup.HC is the pseudo-reduced temperature (calculated
from the black-oil correlations--see below). In this equation,
density is expressed in g/cc, pseudo-reduced temperature is
dimensionless, and the interfacial tension is in dynes/cm. The same
relationship between variables holds for the interface between any
two substances, e.g., mercury and air. The factor .tau. in the
expression for interfacial tension may also be considered to have
indices because the density difference .DELTA..rho. in the
expression above for .tau. refers to the density difference between
the particular two fluids for which the interfacial tension is
being calculated. Once the hydrocarbon-brine interfacial tension
and entry pressure are known, seal capacity may be estimated
according the relationship:
M I C P .eta. Hg - air cos .theta. Hg - air = O E P .eta. B - O cos
.theta. B - O = G E P .eta. B - G cos .theta. B - G ##EQU00003##
where MICP=P.sub.Hg-P.sub.air,
OEP=P.sub.o-P.sub.w,
GEP=P.sub.g-P.sub.w, and [0110] .theta..sub.ij is the contact angle
for i and j fluid system.
Input Data for Some Embodiments of the Present Inventive
Method:
[0110] [0111] Trap parameters (crest depth, spill depth (syncline,
fault juxtaposition leak, or thief sand), temperature at crest)
[0112] Fluid gradients (oil, gas, water gradients from RFT data or
derived by technique outlined above) [0113] Hydrocarbon column
heights or contact depths (e.g., direct hydrocarbon indicators,
AVO, well penetrations) These steps will now be explained in more
detail. (Note: the terms water and brine are used interchangeably
in the interfacial tension discussions.)
Step 73: Estimate Implied Mercury-Injection Capillary Pressure
(MICP) for Current Realization
[0114] (Note: Capillary entry pressure for the seal of a
hydrocarbon cap is normally specified by the gas entry pressure
(GEP) and the oil entry pressure (OEP), or just one of these if the
trap contains only one hydrocarbon phase. However, MICP is often
desired and useful also, primarily to enable comparisons to
laboratory tests.) [0115] (1) A gas specific gravity at D.sup.CTOC
is found to match observed gas leg pressures using a black oil
model (empirical correlations to determine reservoir fluid
properties from field data taken in this case from McCain Jr., W.
D., "Reservoir-fluid property correlations--state of the art," SPE
Reservoir Engineering 6, 266-272 (1991). [0116] (a) Estimate a
value for the gas specific gravity (.gamma..sub.G.sup.CTOC) at
D.sup.CTOC .gamma..sub.G.sup.CTOC. [0117] (b) Calculate
pseudo-critical pressure (P.sub.pc.sup.CTOC) at D.sup.CTOC by:
[0117]
P.sub.pc.sup.CTOC=756.8-.gamma..sub.G.sup.CTOC(131+3.6.gamma..sub-
.G.sup.CTOC) [0118] (c) Calculate pseudo-critical temperature
(T.sub.pc.sup.CTOC) at D.sup.CTOC by:
[0118]
T.sub.pc.sup.CTOC=169.2-.gamma..sub.G.sup.CTOC(349.5+74.0.gamma..-
sub.G.sup.CTOC) [0119] (d) Calculate pseudo-reduced temperature
(T.sub.pr.sup.CTOC) at D.sup.CTOC by:
[0119] T pr CTOC = ( T CTOC + 459.69 ) T pc CTOC ##EQU00004##
[0120] (e) Calculate pseudo-reduced pressure (P.sub.pr.sup.CTOC) at
D.sup.CTOC by:
[0120] P pr CTOC = P G CTOC P pc CTOC ##EQU00005## [0121] (f)
Calculate gas formation volume factor (B.sub.g):
[0121] B g = 0.00502 Z ( T CTOC + 459.69 ) P G CTOC ##EQU00006##
[0122] (g) Calculate gas in-situ density (.rho..sub.g):
[0122] .rho. g = 0.21870617 ( ( 0.001 ) Bg ) .gamma. G CTOC
##EQU00007## [0123] (h) Compare predicted in-situ gas density to
observed in-situ gas density. [0124] (i) Use the difference between
observed and predicted in-situ density to update the gas specific
gravity guess (.gamma..sub.G.sup.CGOC) at D.sup.CGOC in the first
sub-step of step 73. [0125] (j) Repeat until the solution converges
to obtain a gas gravity that matches observed pressure gradients to
within an acceptable tolerance. [0126] (2) Estimate Top Seal MICP.
[0127] (a) Calculate the brine-oil density contrast at the GOC
(.DELTA..rho..sub.B-G)
[0127] .DELTA..rho..sub.B-G=(.rho..sub.B-.rho..sub.O) [0128] (b)
Use the brine-gas density differences to calculate the Firoozabadi
Tau (.tau.--see Firoozabadi & Ramey, "Surface tension of
water-hydrocarbon systems at reservoir conditions," paper no.
87-38-30, presented at the 38.sup.th Annual Technical Meeting of
the Petroleum Society of CIM, Calgary (Jun. 7-10, 1987)).
[0128]
.tau.=e.sup.[0.091251n(.DELTA..rho..sup.B-G.sup.).sup.2.sup.-0.53-
8331n(.DELTA..rho..sup.B-G.sup.)+1.227328] [0129] (c) Use the
Firoozabadi Tau (.tau.) to calculate brine-gas interfacial
tensions.
[0129]
.eta..sub.B-G.sup.CTOC=[.DELTA..rho..sub.B-G(T.sub.pr.sup.CTOC).s-
up.-0.3125.tau.].sup.4 [0130] (d) Calculate an equivalent MICP for
the current realization.
[0130] M I C P = 367.7 G E P CTOC .eta. B - G CTOC ##EQU00008##
Step 74: Estimate the Oil Entry Pressure (OEP) for Current
Realzation
[0131] (1) Find a gas specific gravity at D.sup.CGOC to match
observed gas leg pressures using a black oil model (correlations
from McCain (1991) in this case). [0132] (a) Guess a value for the
gas specific gravity (.gamma..sub.G.sup.CGOC) at D.sup.CGOC. [0133]
(b) Calculate pseudo-critical pressure (P.sub.pc.sup.CGOC) at
D.sup.CGOC by:
[0133]
P.sub.pc.sup.CGOC=756.8-.gamma..sub.B.sup.CTOC(131+3.6.gamma..sub-
.B.sup.CTOC) [0134] (c) Calculate pseudo-critical temperature
(T.sub.pc.sup.CGOC) at D.sup.CGOC by:
[0134]
T.sub.pc.sup.CGOC=169.2-.gamma..sub.G.sup.CGOC(349.5+74.0.gamma..-
sub.G.sup.CGOC) [0135] (d) Calculate pseudo-reduced temperature
(T.sub.pr.sup.CGOC) at D.sup.CGOC by:
[0135] T pr CGOC = ( T CGOC + 459.69 ) T pc CGOC ##EQU00009##
[0136] (e) Calculate pseudo-reduced pressure (P.sub.pr.sup.CGOC) at
D.sup.CGOC by:
[0136] P pr CGOC = P G CGOC P pc CGOC ##EQU00010## [0137] (f)
Calculate gas formation volume factor (B.sub.g):
[0137] B g = 0.00502 Z ( T CGOC + 459.69 ) P G CGOC ##EQU00011##
[0138] (g) Calculate gas in-situ density (.rho..sub.g):
[0138] .rho. g = 0.21870617 ( 0.001 B g ) .gamma. G CGOC
##EQU00012## [0139] (h) Compare predicted in-situ gas density to
observed in-situ gas density [0140] (i) Use the difference between
observed and predicted in-situ density to update gas specific
gravity guess (.gamma..sub.G.sup.CGOC) at D.sup.CGOC in the first
sub-step of step 74. [0141] (j) Repeat until the solution converges
to obtain a gas gravity that matches observed pressure gradients to
within an acceptable tolerance. [0142] (2) Find an oil API gravity
(.gamma..sub.API.sup.CGOC) to match the observed oil leg pressures
using a black oil model (correlations from McCain (1991) assuming
saturation in this case). [0143] (a) Guess a value for the oil API
gravity (.gamma..sub.API.sup.CGOC) at D.sup.CGOC. [0144] (b)
Calculate the oil specific gravity (.gamma..sub.O.sup.CGOC) at
D.sup.CGOC.
[0144] .gamma. O CGOC = 141.5 ( .gamma. API + 131.5 ) ##EQU00013##
[0145] (c) Assuming saturation, calculate the solution gas/oil
ratio (R.sub.s) at D.sup.CGOC.
[0145] R S CGOC = .gamma. G CGOC [ ( P G CGOC 18.2 + 1.4 ) 10 (
0.0125 p API - 0.0091 T CGOC ) ] ( - 0.83 ) ##EQU00014## [0146] (d)
Calculate the saturated oil formation volume factor at the
bubblepoint (B.sub.ob).
[0146] B ob = 0.9759 + 0.00012 [ R S ( .gamma. G CGOC .gamma. O
CGOC ) + 1.25 T CGOC ] 1.2 ##EQU00015## [0147] (e) Calculate oil
in-situ density (.rho..sub.o):
[0147] .rho. O = ( .gamma. O CGOC + 0.0002179 * R S CGOC .gamma. G
CGOC ) B ob ##EQU00016## [0148] (f) Use difference between observed
and predicted in-situ density to update oil API gravity guess
(.gamma..sub.API.sup.GOC) at D.sup.CGOC in sub-step (a). [0149] (g)
Repeat until solution converges to obtain a
.gamma..sub.API.sup.CGOC that matches observed pressure gradients.
[0150] (3) Calculate the OEP from the GEP. [0151] (a) Calculate the
molecular weight of the dead oil (M.sub.O.sup.STP).
[0151]
M.sub.O.sup.STP=433.646-10.1264(.gamma..sub.API.sup.CGOC-20.557)
[0152] (b) Calculate the critical temperature of the dead oil
(T.sub.C.sup.STP).
[0152]
T.sub.C.sup.STP=23.8326281n(M.sub.O.sup.STP).sup.2+166.4536841n(M-
.sub.O.sup.STP)-300.639467 [0153] (c) Calculate the weight fraction
of solution gas (f.sub.G.sup.GOC)
[0153] f G CGOC = ( R S CGOC 379.6 ) ( ( R S CGOC 379.6 ) + 350.565
( .gamma. O CGOC M O STP ) ) ##EQU00017## [0154] (d) Calculate the
critical temperature of the live oil (T.sub.C.sup.CGOC) at
D.sup.CGOC.
[0154]
T.sub.C.sup.CGOC=f.sub.G.sup.CGOCT.sub.pc.sup.CGOC+T.sub.C.sup.ST-
P(1-f.sub.G.sup.CGOC) [0155] (e) Calculate the pseudo-reduced
temperature of the live oil (T.sub.pr.sup.CGOC) at D.sup.CGOC.
[0155] T pr CGOC = ( T CGOC + 459.69 ) T C CGOC ##EQU00018## [0156]
(f) Calculate the brine-oil density contrast at the GOC
(.DELTA..rho..sub.O-B.sup.CGOC).
[0156] .DELTA..rho..sub.B-O=(.rho..sub.B-.rho..sub.O) [0157] (g)
Use the brine-oil density differences to calculate the Firoozabadi
Tau (.tau.).
[0157]
.tau.=e.sup.[0.091251n(.DELTA..rho..sup.B-O.sup.).sup.2.sup.-0.53-
8331n(.DELTA..rho..sup.B-O.sup.)+1.227328] [0158] (h) Use the
Firoozabadi Tau (.tau.) to calculate oil-brine interfacial
tensions.
[0158]
.eta..sub.B-O.sup.CGOC=[.DELTA..rho..sub.B-O(T.sub.pr.sup.CGOC).s-
up.-0.3125.tau.].sup.4 [0159] (i) Calculate the oil entry
pressure.
[0159] O E P CGOC = M I C P ( .eta. B - O CGOC ) 367.7
##EQU00019##
Step 75: Obtain Statistical Distribution of Seal Capacity Estimates
for Calibration Location
[0160] Repeat steps 71-74 a predetermined number of times,
averaging the results and calculating an uncertainty spread in
MICP, GEP.sup.CTOC, and OEP.sup.CGOC.
Step 76: Combine Distributions of Seal Capacity Estimates from any
Other Calibration Locations
[0161] Repeat steps 71-75 for each calibration location summing the
probability distributions for MICP, GEP.sup.CTOC, and
OEP.sup.CGOC.
[0162] The person skilled in the art will recognize that the
preceding embodiment also has value, compared to traditional
approaches, as a stand alone method for estimating capillary seal
capacity, either with the uncertainty estimate, or if desired,
without. In the latter case in its most direct form, input
parameter values would need to be selected in step 71, but for the
prospect location. Then, steps 72-74 would be performed as
described above.
Estimating Hydraulic Fracture Pressure (Step 62)
[0163] A detailed discussion follows of a preferred embodiment for
estimating the mechanical seal capacity and associated uncertainty
at a calibration location.
[0164] The basis for the deterministic mechanical seal capacity
calculation resides with an evaluation of the effective stress of
the reservoir at the top of the hydrocarbon column. As reservoir
fluid pressures increase (i.e., hydraulic pressure at the top of
the hydrocarbon column height increases), the effective stress
decreases and there is an increased risk that the reservoir fluid
pressure may open tensile fractures in the top seal (reservoir
fluid pressures at this point equal or exceed the hydraulic
fracture pressure, or P.sub.f), thereby allowing hydrocarbons to
escape. Two common occurrences increase the hydraulic pressure at
the top of the hydrocarbon column: 1) an increase in hydrocarbon
column height; and 2) an increase in reservoir aquifer pressure
associated with an existing hydrocarbon column.
[0165] The techniques of the embodiment being described assist with
the use of contact information to calculate mechanical seal
capacity with respect to minimum compressive stress. This preferred
embodiment is based on work by Mandl and Harkness, "Hydrocarbon
migration by hydraulic fracturing" in Deformation of Sediments and
Sedimentary Rocks, Geological Special Publication 29, 39-54, Jones
and Preston, Ed's (1987) and Miller, T. W., "New insights on
natural hydraulic fractures induced by abnormally high pore
pressures," AAPG Bulletin 79, 1005-1018 (1995). These workers
established a purely deterministic method to estimate the size of a
hydrocarbon column necessary to hydrofracture the top seal of a
trap, and to identify possible controls on single-phase hydrocarbon
column heights.
[0166] Hydraulic fracture pressure is prescribed as a functional
relationship between pressure and depth. This relationship may be
manually specified by the user based on a priori knowledge. In
other embodiments of the invention, this relationship may be
calculated by at least two means: a linear "least-squares"
regression to LOT (leak-off test) data or through determination of
.sigma..sub.h min as described previously herein.
Input Quantities
[0167] For empirical hydraulic fracture pressure estimation, the
following inputs are used in some embodiments of the invention:
[0168] Leak-off test data from calibration location(s). [0169]
Operational data, such as lost returns incidents, from calibration
location(s).
[0170] For theoretical hydraulic fracture pressure estimation, the
following inputs are used in some embodiments of the invention:
[0171] Lithostatic pressure as a function of depth with uncertainty
range (P.sub.Lith). [0172] Pore pressure as a function of depth
with uncertainty range (P.sub.Pore). [0173] Ratio of minimum and
maximum effective stress (k.sub.o) with uncertainty range.
[0174] The empirical hydraulic fracture pressure estimation may be
performed by following the following basic steps: [0175] (1) Plot
the empirical data as a function of depth. [0176] (2) Calculate (a)
simple best-fit linear regression line(s), minimizing the
sum-of-squares of the vertical distances between the points and the
line(s) by a technique such as that outlined in Davis, Statistics
and Data Analysis in Geology, 2.sup.nd Edition, John Wiley and
Sons, Inc., USA, 176-204 (1986). [0177] (3) Calculate standard
confidence intervals, deriving a relationship between depth and
fracture pressure with associated uncertainties by a technique such
as that outlined in Davis (1986).
[0178] The theoretical hydraulic fracture pressure estimation may
be performed by following the following basic steps: [0179] (1)
Plot P.sub.Lith and P.sub.Pore with associated uncertainty ranges
as a function of depth. [0180] (2) Calculate vertical effective
stress (.sigma..sub.eff=P.sub.Lith-P.sub.Pore) and associated
uncertainty range. [0181] (3) Calculate the minimum horizontal
stress (.sigma..sub.h min) and associated uncertainty range
via:
[0181] .sigma..sub.h min=k.sub.o.sigma..sub.eff+P.sub.pore [0182]
where
[0182] k o = .sigma. 3 - P pore .sigma. 1 - P pore ##EQU00020##
(for a uniaxial compressive state where compaction is in one
direction with no lateral strains)=ratio of minimum and maximum
effective stress; approximately 0.4 for strong materials to >0.8
for shale/clay. [0183] (4) Repeat to determine minimum, most
likely, and maximum values for .sigma..sub.min as a function of
depth.
Probabilistic Calculation of Column Heights (Steps 64-67)
[0184] Steps 61 and 62 of a preferred embodiment have been
described in detail, and with those descriptions, also step 63.
These steps result in probability-weighted distributions for trap
and fluid parameters at the prospect location, capillary entry
pressure from calibration location(s), and hydraulic fracture
pressure from calibration location(s). Next is the probabilistic
procedure. A key to this analysis is recognition that the
probability-weighted distributions of mechanical and capillary seal
capacities must be adjusted to account for differences between the
trap and fluid parameters at the calibration location and those
selected in each realization of the prospect parameter
distribution. In preferred embodiments of the invention,
uncertainty distributions are assigned to all input parameters. The
uncertainties are propagated throughout the analysis, enabling a
statistical analysis of probabilistic simulation for risking and
assessment.
[0185] Input quantities for the probabilistic calculation steps
include the following.
Probability weighted distributions of prospect trap parameters
(from step 63): [0186] Top of column (D.sup.PTOC). [0187] Spill
(D.sup.W). [0188] Prospect temperature (T.sup.PTOC) at D.sup.PTOC.
[0189] Prospect water depth (D.sup.W). Probability weighted
distributions of prospect fluid parameters (from step 63): [0190]
In-situ oil density (.rho..sub.O) [0191] In-situ gas density
(.rho..sub.G) [0192] In-situ brine density (.rho..sub.B) [0193]
Formation pore excess pressure (P.sub.E) Probability weighted
distributions of capillary entry pressure (from step 61): [0194]
MICP Multiple fracture pressure vs. depth curves with associated
confidence intervals (from step 62).
[0195] Following are steps in the preferred embodiment of the
probabilistic calculation, with number references to the flow chart
of FIG. 6.
Randomly Select a Value from Input Parameter Distributions (Step
64).
[0196] From selected inputs, calculate:
[0197] a) Brine pressure at D.sup.PTOC.
P.sub.B=.rho..sub.SWgD.sup.W+.rho..sub.BgD.sup.PTOC+P.sub.E
Revise Oil Entry Pressure (OEP) and Gas Entry Pressure (GEP)
Calculated from the Calibration Location(s) for Present Realization
Prospect Conditions (Step 65). [0198] (1) Calculate the prospect
gas entry pressure from the MICP value determined from the
calibration location(s), evaluating the gas properties at
D.sup.PTOC: [0199] (a) Find a gas gravity (.gamma..sub.G) that
produces the selected in-situ density (.rho..sub.G) as in step 73
of FIG. 7. [0200] (b) Calculate the pseudo-critical gas temperature
(T.sub.pc) by:
[0200] T.sub.pc=169.2+.gamma..sub.G(349.5-74.gamma..sub.G) [0201]
(c) Calculate pseudo-reduced gas temperature (T.sub.pr.sup.PTOC)
by: [0202] (d) Calculate the brine-gas density contrast
(.DELTA..rho..sub.B-G):
[0202] .DELTA..rho..sub.B-G=(.rho..sub.B-.rho..sub.G) [0203] (e)
Use the brine-gas density difference to calculate the Firoozabadi
Tau (.tau.).
[0203]
.tau.=e.sup.[0.091251n(.DELTA..rho..sup.B-G.sup.).sup.2.sup.-0.53-
8331n(.DELTA..rho..sub.B-G.sup.)+1.227328] [0204] (f) Use the
Firoozabadi Tau (.tau.) to calculate brine-gas interfacial
tension.
[0204]
.eta..sub.B-G.sup.PTOC=[.DELTA..rho..sub.B-G(T.sub.pr.sup.PTOC).s-
up.-0.3125.tau.].sup.4 [0205] (g) Use the brine-gas interfacial
tension (.eta..sub.B-G.sup.PTOC) at the prospect D.sup.PTOC to
calculate the GEP at the prospect D.sup.PTOC:
[0205] G E P PTOC = ( .eta. B - G PTOC ) M I C P 367.7 ##EQU00021##
[0206] (2) Calculate the prospect oil entry pressure from the MICP
value determined from the calibration location(s), evaluating the
oil properties at D.sup.PTOC: [0207] (a) Find an oil API gravity
(.gamma..sub.API.sup.PTOC) and an oil specific gravity
(.gamma..sub.O.sup.PTOC) to match selected in-situ density using a
black oil model as in step 74 of FIG. 7. [0208] (b) Assuming
saturation, calculate the solution gas/oil ratio (R.sub.s.sup.PGOC)
at D.sup.PTOC:
[0208] R s PTOC = .gamma. G [ ( P B PTOC 18.2 + 1.4 ) 10 ( 0.0125
.gamma. API PTOC - 0.0091 T PTOC ) ] ( - 0.83 ) ##EQU00022## [0209]
(c) Calculate effective molecular weight (M.sub.Weff).
[0209] M.sub.Weff=433.646-10.1264(.gamma..sub.API.sup.PTOC-20.557)
[0210] (d) Calculate the critical temperature of the dead oil
(T.sub.C.sup.STP)
[0210] T.sub.C.sup.STP=23.832628 log(M.sub.Weff).sup.2-0.53833
log(M.sub.Weff)+1.227328 [0211] (e) Calculate the weight fraction
of solution gas (f.sub.G.sup.PGOC)
[0211] f G PTOC = ( R s PTOC 379.6 ) ( ( R s PTOC 379.6 ) + 350.565
( .gamma. O PTOC M Weff ) ) ##EQU00023## [0212] (f) Calculate the
critical temperature of the live oil (T.sub.C.sup.PGOC) at
D.sup.PGOC.
[0212]
T.sub.C.sup.PTOC=f.sub.G.sup.PTOCT.sub.pc.sup.PTOC+T.sub.C.sup.ST-
P(1-f.sub.G.sup.PTOC) [0213] g) Calculate the pseudo-reduced
temperature of the live oil (T.sub.pr.sup.PTOC) at D.sup.PTOC.
[0213] T pr PTOC = ( T PTOC + 459.6 ) T C PTOC ##EQU00024## [0214]
h) Calculate the brine-oil density contrast
(.DELTA..rho..sub.O-B.sup.PTOC).
[0214]
.DELTA..rho..sub.B-O.sup.PTOC=(.rho..sub.B-.rho..sub.O.sup.PTOC)
[0215] i) Use the brine-oil density differences to calculate the
Firoozabadi Tau (.tau.).
[0215]
.tau.=e.sup.[0.091251n(.DELTA..rho..sup.B-O.sup.PTOC.sup.).sup.2.-
sup.-0.538331n(.DELTA..rho..sup.B-O.sup.PTOC.sup.)+1.227328] [0216]
j) Use the Firoozabadi Tau (.tau.) to calculate oil-brine
interfacial tensions.
[0216]
.eta..sub.B-O.sup.PTOC=[.DELTA..rho..sub.B-O.sup.PTOC(T.sub.pr.su-
p.PTOC).sup.-0.3125.tau.].sup.4 [0217] k) Calculate the oil entry
pressure.
[0217] O E P PTOC = ( .eta. B - O PTOC ) M I C P 367.7
##EQU00025##
Revise Hydraulic Fracture Pressure Based Upon Selected Trap
Parameters in the Present Realization (Step 66).
[0218] 1) For empirical hydraulic fracture pressure model (from
step 62), calculate a probability-weighted distribution of
hydraulic fracture pressure at D.sup.PTOC: [0219] (i) Referring to
FIG. 8, equate best-fit (preferably in a least-squares sense)
regression line 81 and 68.27% standard confidence intervals 82
determined at the estimated crest depth 84 of the subject trap,
D.sup.PTOC, to specify the mean 86 and one standard deviation 87 of
a normal (Gaussian) distribution 85 of hydraulic fracture
pressures. This determines the topology of the normal distribution
curve from which the random trials will select hydraulic fracture
pressures. The fracture pressure data points 83 plotted in FIG. 8
may be obtained, for example, from leak-off tests conducted at the
calibration location(s). The estimate of the subject trap's crest
depth may be obtained, for example, from seismic data. [0220] (ii)
Randomly select from the probability-weighted distribution from
step (i) a hydraulic fracture pressure value (P.sub.f) for the
present realization. [0221] 2) For hydraulic theoretical fracture
pressure model (from step 62), calculate a probability-weighted
distribution of hydraulic fracture pressure at D.sup.PTOC [0222]
(i) Referring to FIG. 9, equate most likely 91, minimum 92, and
maximum 93 .sigma..sub.h min (i.e., P.sub.Frac) determined at the
estimated crest depth 95 for the subject trap, D.sup.PTOC, to
specify the most likely, minimum, and maximum values on a
triangular distribution 94 of fracture pressures. The theoretical
fracture pressure model is used to generate the curves 96, 97 and
98. [0223] (ii) Randomly select from this probability-weighted
distribution a hydraulic fracture pressure value (P.sub.f) for the
present realization. Calculate Hydrocarbon Column Heights
Consistent with Trap Parameters, Fluid Parameters, Hydraulic
Fracture Pressure, OEP, and GEP in Present Realization (Step
67).
[0224] Alternative potential cases are depicted in FIGS. 5A-F. The
procedure requires equating the calculated OEP and GEP to the
buoyancy of the hydrocarbon column relative to the associated
aquifer pressure gradient for capillary seal capacity, and equating
the absolute pressure at the top of the hydrocarbon column (trap
crest) to P.sub.f at the top of the column (trap crest) for
mechanical seal capacity. The height of the hydrocarbon column
(gas, oil, or combination of both) required to achieve the
necessary buoyancy or absolute pressure is the seal capacity for
that realization.
Repeat Steps 74-77 to Obtain More Realizations (Step 68). (Self
Explanatory)
CONCLUSION
[0225] The foregoing application is directed to particular
embodiments of the present invention for the purpose of
illustrating it. It will be apparent, however, to one skilled in
the art, that many modifications and variations to the embodiments
described herein are possible. For example, a probability-weighted
distribution which is random sampled in the present invention may
be a single value assigned a probability of unity. Furthermore, it
should be apparent to persons skilled in the art that detailed
explanations presented hereinabove of how the steps of FIGS. 6 and
7 might be performed constitute but one or a few specific
embodiments of the present inventive method, and are not intended
to limit the broader description in the claims which is drafted to
include all embodiments. To disclose all embodiments at this same
level of detail would be both (a) impossible and (b) unnecessary
for the understanding of the skilled practitioner. All such
modifications and variations are intended to be within the scope of
the present invention, as defined in the appended claims. The
reader skilled in the art will also recognize that the invention
will preferably be practiced with computer implementation, meaning
that at least some parts of the method are performed on a
computer.
TABLE-US-00001 Glossary of Abbreviations B.sub.g Formation volume
factor of dry gas, res ft.sup.3/scf or RB/scf B.sub.ob Saturation
oil formation volume factor, RB/STB D Depth (ft) f Weight fraction
g Gravitational constant GEP Gas entry pressure (psi) IFT
Interfacial tension (dynes/cm.sup.2) k.sub.o lithology dependent
horizontal to vertical stress ratio MICP Mercury-injection
capillary pressure OEP Oil entry pressure (psi) P Pressure (psi)
R.sub.s Solution gas-oil ratio T Temperature (.degree. F.) Z Z
factor Symbols .gamma. Specific gravity (w/respect to air for gas
or water for oil) e .eta. Interfacial tension .rho. Density
(g/cm.sup.3) .sigma. Stress (psi) .sigma..sub.eff Effective stress
(psi) .sigma..sub.hmin Horizontal minimum stress (psi)
.sigma..sub.1 Maximum compressive stress .sigma..sub.3 Minimum
compressive stress .tau. Firoozabadi tau Superscripts TOC Top of
column OWC Oil-water contact GOC Gas-oil contact C Calibration
location P Prospect location STP Standard temperature and pressure
(60.degree. F., 14.65 psia) Subscripts API American Petroleum
Institute B Brine O Oil G or g Gas lith Lithostatic pore Pore pc
Pseudo-critical pr Pseudo-reduced F or f Fracture Hg Mercury a
Air
* * * * *